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A generalized mixed type of quartic-cubic-quadratic-additive functional equations. (English. Russian original) Zbl 1247.39023
Let $k\not\in\{0,\pm 1\}$ be a fixed integer. The authors give the general solution of the functional equation $$ f(x+ky)+f(x-ky)=g(x+y)+g(x-y)+h(x)+h(y). $$ In fact, the main result of the paper is a straightforward consequence of a particular case of {\it L. Székelyhidi}’s result [Convolution type functional equations on topological abelian groups, Singapore etc.: World Scientific (1991; Zbl 0748.39003)].

39B22Functional equations for real functions
39B52Functional equations for functions with more general domains and/or ranges
Full Text: DOI
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